# Research Group of Prof. Dr. Frans R. Klinkhamer

Focus: fundamental aspects of elementary particle physics and structure of spacetime

## 1. Baryon number violation through nonperturbative effects in the Electroweak Standard Model:

Sphalerons and spectral flow:

New results on spectral flow and sphalerons have been obtained in [Klinkhamer & Lee, 2001] and are under investigation.

The sphaleron $\text{S}$ is related to the Adler-Bell-Bardeen anomaly. Over the years, it has become clear that there are more sphalerons. In fact, there also exists a sphaleron $\text{S}^{*}$ related to the $SU(2)$ Witten anomaly; see [Klinkhamer, 1993]. And, finally, there exists a sphaleron $\widehat{\text{S}}$ related to the $SU(3)$ Bardeen anomaly; see [Klinkhamer & Rupp, 2005; Klinkhamer & Nagel, 2017].

## 2. CPT anomaly:

Chiral gauge theories defined over a topologically nontrivial space manifold have an anomalous breaking of Lorentz and CPT invariance. An extensive review: [Klinkhamer, 2005].

 Cosmology [Klinkhamer, 2001; Klinkhamer, 2002]: optical activity of the vacuum arrow-of-time (see sketch on the right)

## 3. Small-scale structure of spacetime:

The goal is to investigate a possible nontrivial structure of spacetime at very small length scales.

 Two aspects have been considered in particular: The impact on the propagation of photons with wavelengths larger than the size of the "spacetime defects" (see, e.g., [Bernadotte & Klinkhamer, 2007; Klinkhamer & Schreck, 2008; Klinkhamer et al., 2017]). The detailed structure of one particular type of "spacetime defect" appearing as a soliton-type solution of the classical field equations (for a review, see [Klinkhamer, 2018]).

## 4. Vacuum energy and cosmology:

Since 1998, it has become clear that there is not one cosmological constant problem but that there are three:

• Why is |ρvac| << (EPlanck)4 ?
• Why is ρvac ≠ 0 ?
• Why is now ρvac ∼ ρmatter ?

Taking Lorentz-invariance seriously (cf. recent UHECR bounds on Lorentz violation in the photon sector [Klinkhamer et al., 2017]), a new approach [Klinkhamer & Volovik, 2008] to this set of problems is based on the following assumption:

the perfect quantum vacuum can be considered to behave as a self-sustained Lorentz-invariant medium with a new type of conserved charge.

The argument is based solely on thermodynamics (cf. Einstein 1907) and has an analog in condensed-matter physics (Larkin-Pikin effect, 1969).

Recent results are reviewed in [Klinkhamer & Volovik, 2016; Klinkhamer & Volovik, 2019].

Some talks:
1. Cosmological constant problem: Revisiting the unimodular-gravity approach (Athens, October 2022)
2. IIB matrix model, bosonic master field, and emergent spacetime (Corfu, September 2021)
3. M-theory and the birth of the Universe (Cracow, January 2021)
4. Spacetime defects (Castiglioncello, September 2018)
5. On an anomalous origin of Lorentz and CPT violation (Faro, July 2017)
6. A new approach to the cosmological constant problem (Seoul, October 2015; Update January 2019)
7. Sphalerons and anomalies (an introduction) (Seoul, October 2015)
8. Elementary particle physics and cosmology for engineers (and others) (Karlsruhe, February 2013)
9. Superluminal neutrino: Theoretical considerations (Karlsruhe, December 2011)
10. Towards a derivation of G (Bremen, July 2010)
11. UHECR bounds on Lorentz violation in the photon sector (Penn State, August 2008)
12. Lorentz noninvariance and neutrino oscillations (Belgium, February/March 2006)
13. Nontrivial spacetime topology, CPT violation, and photons (Lisbon, July 2005)
14. Electroweak baryon number violation: basic mechanism (Ann Arbor, June 2003)